Select Quads and remove them
It could depend also on the resulting mesh you wish to obtain, eg: 


a big plane with only 4 vertices?
a big empty plane with only 4 vertices?
the plane as it is but without inner quads?


see a couple of example below, using dissolve commands

with dissolve vertices, but you get a plane of more than 4 verts





or with dissolve edges





...you get the idea...

[edit]
in the tutoarial you are following inthe link above, it says 

"Create a plane, subdivide it two times and then remove the inner four quads."

well, 


first, it is wrong: to get the subdivided plane I see in that image, which has a total of 16 face after subdivision, you have to subdivide the plane 3 times, not 2.


then it seems to convert those inner 4 faces into a a big square.

so you can switch to select faces mode, selet the inner 4 faces, and simply "dissolve faces"... like this